Intrusions in Stratified Fluid

Experiments/Research performed by Chris Voegeli,
May - August 2005,
Department of Mathematical and Statistical Sciences, University of Alberta

Background

Witnessing a body of fog move over a highway at night or seeing a cloud pour over a mountain (as in picture above) are events most people are familiar with. Observing such spectacles is infact to bear witness to a gravity current.

When a body of fluid is stratified the fluid density effectively decreases from the bottom to the top.If the rate at which the density changes with heigth is linear the fluid is said to be uniformly stratified.The stratosphere is strongly stratified, which is why airplanes chose to fly through it for it's stabilty.

When a homogenous body of fluid of a certain density moves horizontally within a stratified fluid it is called an intrusion. If this propagation moves along the base of a stratifeid or unstratified fluid it is called a gravity current. Typically an intrusion propogates along a fluid layer that has the same density.

Although fluid dynamicists and engineers have studied gravity currents extensively, dynamics of intrusions in stratified fluids has had little exploration. Exploring intrusion dynamics will give insigths inot small scale phenomena in oceanography, metereology, and industry.

Experimental Setup and Analysis Methods

The experiments were performed in a rectangular tank measuring 48.8cm in height, 17.4cm in width, and 197.3 cm in length. The tank was filled to a predetermined height with uniformly stratified fluid using a standard double bucket system. For the purpose of visual analysis, every 5cm during filling food colouring was added, which would disperse in a horizontal plane in the stratified fluid.

Once the tank is filled a conductivity probe traverses vertically through the tank to measure the density profile.

A gate was then inserted close to the left end of the tank and the fluid in this lock was well mixed. If the experiment called for the lock density to be the average density of the stratified fluid only dye was added. Otherwise some salt and dye was added to the lock so that when the gate is released the resulting intrusion would propagate below mid-depth.

A video camera records the collapse of the lock fluid into the ambient and the resulting displacement of dye lines.

Every experiment that was done explored 4 parameters. Fluid depth(H), lock length(L), density of the bottom of stratified fluid body(PB), and density of fluid in the lock (PL).

Once the experiment was completed the film was then digitized and analysed. The analysis was done by taking horizontal time series (HTS) and vertical time series (VTS). These analyses were used to measure intrusion speed and size as well as internal wave speeds, amplitudes and wavelengths.

Results

The results presented here include 3 experiments with the following 3 fixed parameters. H=30cm, L=18.5cm, and PB=1.15. From left-to-right, the lock density (PL) is at 1.075g/L, 1.1125g/L, and 1.15g/L. Below are 3 videos of the intrusions and corresponding horizontal and vertical time series.

video of mid-depth intrusion	video of 3/4 depth intrusion	video of bottom-depth intrusion

H=30cm L=18.5cm PB=1.15 PL=1.075	H=30cm L=18.5cm PB=1.15 PL=1.1125	H=30cm L=18.5cm PB=1.15 PL=1.15
HTS at depth of intrusion	HTS at depth of intrusion	HTS at depth of intrusion

HTS at z=25cm	HTS at z=25cm	HTS at z=25

VTS at x=60cm	VTS at x=60cm	VTS at x=60cm

Analysis of our results reveals that the intrusion speed increases as more salt is added to the lock. We find the speed of waves in the tank increases at a greater rate when a small amount of salt is added, but the two speeds are the same by the time enough salt is added that the intrusion moves along the bottom of the tank. This helps explain why the intrusion stops propagating when it propagates between half-depth and the tank bottom: waves are able to carry energy away from the current in such cases.

Links to related research

This work is an extension of earlier experimental research into intrusions in two-layer and three-layer fluids:

Axisymmetric Intrusive Gravity Currents,
B. R. Sutherland, J. Nault and L. Blackburn, Phys. Fluids
Internal Wave Excitation from a Collapsed Mixed Region,
B. R. Sutherland, M. R. Flynn and K. Dohan, Deep-Sea Res. II, 51, pp 2889-2904 (2004)
Intrusive Gravity Currents and Internal Gravity Wave Generation in Stratified Fluid,
M. R. Flynn and B. R. Sutherland, J. Fluid Mech. 514, pp 355-383 (2004).
Intrusive Gravity Currents in Two-layer Fluids,
B. R. Sutherland, P. J. Kyba and M. R. Flynn, J. Fluid Mech. 514, pp 327-353 (2004).
Interfacial Gravity Currents: Part II - Wave Excitation,
A. P. Mehta, B. R. Sutherland and P. J. Kyba, Phys. Fluids, 14, pp 3558-3569 (2002).
Interfacial Gravity Currents: Mixing and Entrainment,
B. R. Sutherland, Phys. Fluids, 14, pp 2244-2254 (2002).

Acknowledgements

NSERC, CFCAS

Department of Math and Statistical Sciences, University of Alberta

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